The problem of the process of coupled diffusion and reaction in catalyst pellets is considered for the case of second and half order reactions. The Adomian decomposition method is used to solve the non-linear model. For the second, half and first order reactions, analytical approximate solutions are obtained. The variation of reactant concentration in the catalyst pellet and the effectiveness factors at φ< 10 are determined and compared with those by the BAND’s finite difference numerical method developed by Newman. At lower values of φ, the decomposition solution with 3 terms gives satisfactory agreement with the numerical solution; at higher values of φ, as the term number in the decomposition method is increased, an acceptable agreement between the two methods is achieved. In general, the solution with 6 terms gives a satisfactory agreement. The problem of the process of coupled diffusion and reaction in catalyst pellets is considered for the case of second and half order reactions. The Adomian decomposition method is used to solve the non-linear model. For the second, half and first order reactions, analytical The variation of reactant concentration in the catalyst pellet and the effectiveness factors at φ <10 are determined and compared with those by the BAND’s finite difference numerical method developed by Newman. At lower values ​​of φ, the decomposition solution with 3 at generalization of the numerical solution; at higher values ​​of φ, as the term number in the decomposition method is increased, an acceptable agreement between the two methods is achieved.